Forest, --- Forest Simmons <[EMAIL PROTECTED]> a écrit : > I haven't had time to give these new 3-slot ideas too much thought yet, > but my first question is, "Which of them satisfy the (weak) FBC?" > > MCA and 3-slot CR both satisfy the (weak) FBC, but do any of these newer > methods?
I put some thought into this question today, and my answers are not very happy ones. Glad you asked, though. The unnamed runoff method I most recently posted fails weak FBC badly. I should've thought about that one a bit more. There's a problem in mixing approval defeats with pairwise defeats. If Favorite beats Compromise by approval, and it causes a cycle to be resolved in favor of Worst, you can't fix that by ranking Favorite=Compromise. You have to take away Favorite's approval to break the cycle. MAR fails weak FBC, it seems, because of the majority cutoff, and the fact that the second round method doesn't meet IIA. That is, it might be advantageous to keep a (liked, but losing) candidate from meeting the cutoff, in order to transfer the win to some compromise. MAFP is the only method that meets weak FBC, because the second round is unaffected by deleting losers. Thus disapproving Favorite can only hurt Favorite, and not help anyone else. However, a little thought has led me to realize that MAFP is just MCA on its head. When multiple candidates have a median rating of "middle" in MCA, the one with the fewest "worst" ratings is elected. In MAFP, it's the one with the most "top" ratings. Is this better? It doesn't really seem like it! ...Back to the drawing board, I suppose. Kevin Venzke [EMAIL PROTECTED] ___________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français ! Yahoo! Mail : http://fr.mail.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info